Causal Models At Work

AIDS Specialist: You know, people think AIDS is a death sentence. But how long do you think the average person lives after getting HIV?Me: I don’t know.AIDS Specialist: Thirty years! Isn’t that amazing? You can get HIV, and probably you’ll live another three decades!Me: Really?AIDS Specialist: Yeah.Me: So, the trick is, give yourself HIV when you’re eighty, then live to be a hundred ten.AIDS Specialist: I like you.Me: Really?AIDS Specialist: No.

And a few weeks later:

Me: Do you have a family history of alcoholism?Alcoholic Patient: No. Why?Me: Well, I am trying to figure out whether to prescribe you this medication, and studies suggest it works best in patients with a genetic predisposition to alcohol abuse.Alcoholic Patient: I don’t understand.Me: The medicine only works if one of your parents drinks too much.Alcoholic Patient: Well, I think I can get my dad to start.Me: NO!

No. Think of it this way: take away the “after getting HIV” part. How long does the average person in the U.S. have to live starting from this point? Well, the median person in the U.S. is 40. Life expectancy at 40 is about 38 more years. So the average person has a life expectancy of about 38 more years But doesn’t mean someone at 15 has a life expectancy of 38 more years: someone at 15 has a life expectancy of 62 more years. It’s the same with HIV. The distribution of number of years that people live after being diagnosed with HIV varies with age of diagnosis, just as the distribution of life expectancy varies for people who haven’t been diagnosed with HIV.

That would depend on the quality adjustment part, perhaps even more than the life years part. It would probably be easier to measure the difference in expected lifespan upon learning that you had HIV.

That is, if you learn “Bob is a 30-year-old American male”, you’d expect him to live for about 48 more years if you trust the first Google hit for “actuarial chart”. If you then learned Bob had AIDS, what would your new estimate of his lifespan be, and how would this change with the age/gender of Bob?

EDIT: Of course, this isn’t actually the question you want to ask, because of confounders. It’s still probably the most informative one that’s easy to answer (especially if you care about being ethical while answering the question).

What Daniel suggests would be the measure I’d want as well, and I don’t know what that is.
I would argue, though, that this isn’t a totally silly measure just by virtue of the fact that life expectancy after HIV diagnosis used to be so much lower. The major reason why it’s changed is the development of better medications, not the changing age distribution of the newly-infected. If you are remembering those days and thinking that HIV diagnosis still equals impending death, this can inform you otherwise.

The alcoholism example would be legitimate given Lesswrong-style ideas of timeless decision theory (which I don’t necessarily endorse). If you are able to convince your dad to become a drinker, it is more likely that you have a genetic history of alcoholism, even though the genetic history is not caused by the fact that you have convinced him. This does mean convincing your dad to drink will be assicated with a higher chance that the medicine works.

In fact it can be seen on a variation on the smoker’s lesion problem; only the “drinker’s genetic lesion” is associated with something good (better ability to use the drug) instead of something bad (cancer).

I’m pretty sure TD, UD, and ED would take the knowledge that the father can probably be convinced as evidence that the gene is present. Then, given that the convincing happened, it would be further evidence and ED would say this was good for the patient’s chances of having the treatment work. TD and UD would still say that the convincing might be useful from a VoI perspective.

Of course, given that somebody could be convinced to become alcoholic even without the relevent gene, I’m not sure how much evidence this is. It almost certainly would not be good from any of the three theories if you take into account the costs to (presumably) a loved one.

This doesn’t have to be evidential decision theory, if one presents it not as believing that convincing the father to drink ‘affects’ the effectiveness of the treatment but rather that it gives evidence of what that effectiveness would be so as to allow a more informed decision. That’s entirely causal (though not exactly an efficient or ethical use of your time).

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